One-parameter Darboux-transformed quantum actions in Thermodynamics

Transmutations for Darboux transformed operators with applications

We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schrödinger operator. Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schrödinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2. It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. Given a kernel K_1 of the …

Generalization of the Darboux transformation and generalized harmonic oscillators

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N=2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according…

Quantum coherence can be transformed into heat

The first law of thermodynamics restates the law of conservation of energy. It partitions the change in energy of a system into two pieces, heat and work. While there is no ambiguity to define heat and work in classical thermodynamics, their classification in the quantum regime is not that obvious. Thus, the first law of thermodynamics becomes problematic in the quantum regime. However, recent studies have shown if contribution of quantum coherence is considered to the change of internal energy of the system, the first law of thermodynamics can be extended to the quantum domain. Here we invest…

量子Mpemba效应的热力学

Thermodynamics of the quantum Mpemba effect

本研究从非平衡量子热力学角度探究量子Mpemba效应，证明特定条件下量子态变换会带来平衡的指数级加速，还构造出可产生该效应的幺正变换并通过量子比特示例验证。

对单位元变换热库的广义兰道原理

A Generalized Landauer's Principle for Unitarily Transformed Thermal Reservoirs

本文提出广义兰道原理，用于解释压缩热态下的热力学资源影响，通过有效哈密顿量建立广义不等式，并证明熵产非负性，用于研究运动探测器与量子场的相互作用。

Thermodynamics as a Consequence of Information Conservation

Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditiona…